A Ritchey–Chrétien telescope (RCT or simply RC) is a specialized Cassegrain telescope invented in the early 20th century that has a hyperbolicprimary mirror and a hyperbolic secondary mirror designed to eliminate optical errors (coma). They have large field of view free of optical errors compared to a more conventional reflecting telescope configuration. Since the mid 20th century most large professional research telescopes have been Ritchey–Chrétien configurations.

The Ritchey–Chrétien design is free of third-order coma and spherical aberration,[1] although it does suffer from fifth-order coma, severe large-angle astigmatism, and comparatively severe field curvature.[2] When focused midway between the sagittal and tangential focusing planes, stars are imaged as circles, making the RCT well suited for wide field and photographic observations. As with the other Cassegrain-configuration reflectors, the RCT has a very short optical tube assembly and compact design for a given focal length. The RCT offers good off-axis optical performance, but examples are relatively rare due to the high cost of hyperbolic primary mirror fabrication; Ritchey–Chrétien configurations are most commonly found on high-performance professional telescopes.

A telescope with only one curved mirror, such as a Newtonian telescope, will always have aberrations. If the mirror is spherical, it will suffer from spherical aberration. If the mirror is made parabolic, to correct the spherical aberration, then it must necessarily suffer from coma and astigmatism. With two curved mirrors, such as the Ritchey–Chrétien telescope, coma can be eliminated as well. This allows a larger useful field of view. However, such designs still suffer from astigmatism. This too can be cancelled by including a third curved optical element. When this element is a mirror, the result is a three-mirror anastigmat. In practice, each of these designs may also include any number of flat fold mirrors, used to bend the optical path into more convenient configurations.

is the back focal length (the distance from the secondary to the focus), and

is the distance between the two mirrors.

If, instead of and , the known quantities are the focal length of the primary mirror, , and the distance to the focus behind the primary mirror, , then and .

For a Ritchey–Chrétien system, the conic constants and of the two mirrors are chosen so as to eliminate third-order spherical aberration and coma; the solution is

and

where is the secondary magnification.[3] Note that and are less than (since ), so both mirrors are hyperbolic. (The primary mirror is typically quite close to being parabolic, however.)

The hyperbolic curvatures are difficult to test, especially with equipment typically available to amateur telescope makers or laboratory-scale fabricators; thus, older telescope layouts predominate in these applications. However, professional optics fabricators and large research groups test their mirrors with interferometers. A Ritchey–Chrétien then requires minimal additional equipment, typically a small optical device called a null corrector that makes the hyperbolic primary look spherical for the interferometric test. On the Hubble Space Telescope, this device was built incorrectly (a reflection from an un-intended surface leading to an incorrect measurement of lens position) leading to the error in the Hubble primary mirror.[4] Incorrect null correctors have led to other mirror fabrication errors as well, such as in the New Technology Telescope.

Ritchey intended the 100 inch Hooker telescope and the 200-inch (5 m) Hale Telescope to be RCTs. His designs would have provided sharper images over a larger usable field of view compared to the parabolic designs actually used. However, Ritchey and Hale had a falling out. With the 100 inch project already late and over budget, Hale refused to adopt the new design, with its hard-to-test curvatures, and Ritchey left the project. Both projects were then built with traditional optics. Since then, advances in optical measurement[5] and fabrication[6] have allowed the RCT design to take over - the Hale telescope turned out to be the last world-leading telescope to have a parabolic primary mirror.[7]